The present invention relates to the simulation of the reflectometry response from grating profiles and more particularly to an efficient method for accurately simulating the integrated reflectometry response from two-dimensional grating structures using a few points.
Spectroscopic reflectometry and ellipsometry have been a mainstay for thin film metrology for many years. Recently, spectroscopic reflectometry and ellipsometry have been applied to characterizing patterned structures in integrated circuit (IC) processing by directing a beam of light on the patterned structures at a certain angle of incidence and measuring the spectra of the reflected light. However, due to the difficulty of rigorous simulation responses from patterned structures, empirical methods, such as neural networks (NN) or principle component analysis (PCA), are used to build up the relation between the patterned structure parameters (e.g., width of a structure (CD), grating height, sidewall angle, and other profile parameters) and reflected spectra.
FIG. 1 illustrates a typical reflectometry configuration for characterizing patterned structures located on a wafer. A broadband light beam 105 travels through an optical system 110 characterized by a numerical aperture. A lens 115 focuses the broadband light beam 105 into a spot characterized by a spot size onto a patterned structure located on wafer 120 (note that throughout this specification a lens is referred to more generically as an aperture). The light reflected off of the patterned structure located on wafer 120 is then collected by lens 115 and transmitted to a spectrometer 125 through optical system 110. Using other metrology tools, such as a scanning electron microscope (SEM), an atomic force microscope (AFM), etc., the parameters of the patterned structure can be measured off-line. Next, neural networks or principal component analysis can be used to build up (train) a non-linear relation between the reflected spectra and the parameters of the patterned structure. However, the relation between the reflected spectra and the parameters of the patterned structure is only valid when the values of the parameters are within the range of parameters used for training. Furthermore, long turnaround times imposed by off-line metrology also result in lower yields, slower learning curves, and higher costs for new processes and products.
A multi-point rigorous simulation method can be used to avoid doing experiments to build up empirical relations between the reflected spectra and the parameters of patterned structures. Ideally, the numerical aperture should be very small (e.g. less than 0.01) so that the reflectometry response can be simulated using normal incidence. However, if the lens 115 is too small, then the light throughput is low, thus weakening the intensity of the light beam 105 incident on a two-dimensional grating structure. The weaker the intensity of the light beam 105, the longer it takes to collect enough simulation data to achieve stability.
Starting from Maxwell""s equations, the response of light reflected from patterned structures can be simulated rigorously using numerical methods. However, in an actual reflectometry system, to have an acceptable spot size (less than 100 xcexcm) and throughput (less than 1 second), the numerical aperture (NA) is fairly large (about 0.05 or larger). Thus, the reflectance is actually the integrated response from multiple beams of light reflected off the patterned structures, where the incidence angle of each light beam is close to zero degrees. FIGS. 2a and 2b show an example of the multi-point rigorous simulation method. FIG. 2a shows light passing through numerous (e.g., 20 to 30) points 205 across an aperture 210 creating numerous light beams 215. The aperture 210 focuses each light beam 215 onto the two-dimensional grating structure 220 at an angle close to zero degrees. Simulating the numerous light beams 215 focused onto the two-dimensional grating structure 220 yields the response distribution 225 for light beams 215 as shown in FIG. 2b. The integrated response for this wavelength very closely approximates the actual reflectance and can be obtained by adding up each of the responses shown in FIG. 2b. However, the simulation takes a long time.
A single point rigorous simulation method can also be used to avoid doing experiments to build up empirical relations between the reflected spectra and the parameters of the patterned structures. FIGS. 3a and 3b show an example of the single point rigorous simulation method. FIG. 3a shows a simulation of light passing through a single point O 305 located at the center of an aperture 310 creating a single light beam 315. The light beam 315 is incident on the two-dimensional grating structure 320 at an angle of zero degrees. FIG. 3b shows the simulated reflectance response 325 of the light passing through the single point O 305. Although, the reflectance response 325 can be obtained very quickly, it is not very accurate since it only represents the reflectance response 325 from light passing through the single point O 305. The reflectance response 325 does not take into account the reflectance response from light passing through other points across the aperture 310, and thus cannot represent the overall reflectance response of the aperture 310.
FIG. 4 is a simulation which compares the accuracy of the response from light reflected off of a two-dimensional grating structure using the multi-point rigorous simulation method and the single point simulation method. As shown in FIG. 4, the simulated response 410 obtained using the single point rigorous simulation method differs greatly from the response 405 obtained using the multi-point rigorous simulation method. The multi-point rigorous simulation method closely approximates the actual reflectance response. Thus, there is a desire for a method of simulating the reflectance response of two-dimensional grating structures that is both accurate and not time consuming.
The method in accordance with embodiments of the present invention relates to a method for efficient simulation of reflectometry response from two-dimensional grating structures.
In one embodiment, the light intensity distribution across the aperture is uniform. A first and a second point are determined within an aperture located in an optical system. Next, the reflectance response of light incident at the first point and the second point are simulated. The approximated integrated reflectance response of the aperture is then determined based on the reflectance response at the first point and the second point and determined characteristics of the optical system.
In another embodiment, the light intensity distribution across the aperture is not uniform. A first and a second point are determined within an aperture located in an optical system. Next, the reflectance response of light incident at the first point and the second point are simulated. The approximated integrated reflectance response of the aperture is then determined based on the reflectance response at the first point and the second point and determined characteristics of the optical system.